[Technology Exercise] 75. Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bounded by the x-axis, the curve y = arctan(x), and the line x = √3.

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / √(1 - 4x²) from 0 to 1/(2√2)

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (1 / (cos² x tan x)) dx from π/3 to π/4

Evaluate the integrals in Exercises 23–32.

∫₀^π √(1 - cos(2x)) dx

Volume: Find the volume generated by revolving one arch of the curve y = sin x about the x-axis.

In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

∫ from 2 to ∞ of ((1 / ln x) dx)

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ dx / (x √(7 - x²))